Van Aubel's theorem states that if you start with a convex quadrilateral and construct a square on each side, externally to the quadrilateral, then the line segments connecting the centers of opposite squares will be equal in length and perpendicular to each other.
The following images provide a synthetic proof of this theorem. The line segments mentioned are colored in green and red.
The green and red circumference cross on point
The purple line is the perpendiculat to the green line that passes through
This concludes the proof of this theorem.
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